CN105634579A - Multi-antenna two-way relay evidence theory receiving method based on decode-and-forward network coding - Google Patents

Abstract

The invention discloses a multi-antenna two-way relay evidence theory receiving method based on decode-and-forward network coding. The method comprises the following steps: firstly, building a multi-antenna two-way relay model not including a direct link; and then, analyzing performance and defects of an existing multi-antenna two-way relay receiving algorithm based on the decode-and-forward network coding, and providing the multi-antenna two-way relay evidence theory receiving method based on the decode-and-forward network coding according to the defects of the existing algorithm. The method is characterized in that initial decision statistics of a received signal are acquired through a conventional multi-antenna detection method firstly; then, uncertainties generated by a fading channel and noise in the decision statistics of the received signal are described through a basic belief assignment function; the uncertainties of the decision statistics of the received signal are lowered through an evidence theory combining rule; and lastly, a reliable transmission signal is obtained through a maximum value decision criterion. Compared with an existing sub-optimal algorithm, the method has the advantages that the bit error rate performance of a relay receiving end is improved well. Lastly, simulation verification is performed on the algorithm, and a result which is consistent with theoretical analysis is obtained.

Description

Based on the theoretical reception method of multiple antennas bi-directional relaying evidence of decoding transmission network coding

Technical field

The present invention relates to a kind of theoretical reception method of multiple antennas bi-directional relaying evidence based on decoding transmission network coding, the theoretical fusion with decoding transmission network coding by evidence, design a kind of detection algorithm improving multiple antennas bi-directional relaying receiving end performance of BER, belong to the relevant field of collaboration communication to multi-input and multi-output system signal treatment research.

Background technology

Bi-directional relaying technology (two-wayrelay) is widely used as one of the key of collaboration communication technology. It can improve the area coverage of communication system, throughput capacity and reduction energy consumption. Traditional single antenna bi-directional relaying technology completes primary information and exchanges gap when needing four, causes the reduction of spectrum effectiveness. But, along with multiple-input and multiple-output (multiple-inputmultiple-output, MIMO) develop rapidly that technology is done and extensively utilization, the combination of MIMO technology and bi-directional relaying technology can effectively improve spectrum effectiveness, and increases the reliability of communication link. Along with network encodes the further proposition of (networkcoding, NC), the multiple antennas bi-directional relaying based on network coding completes gap when primary information only needs two alternately, is many locations stage and broadcast stage. Many locations stage is that two users send each self-information to relaying node simultaneously, and the broadcast stage is that relaying node sends identical information to two users simultaneously. Therefore, the multiple antennas bi-directional relaying system based on network coding can improve system capacity, throughput capacity and spectrum effectiveness further, and relay reception algorithm is the important factor that system obtains optimal performance reliably.

In multiple antennas bi-directional relaying system, maximum likelihood (maximumlikelihood, the ML) receiving algorithm based on decoding transmission network coding provides optimum receptivity. But, about the number of transmit antennas exponentially complexity of trend growth and the limitation of decoding transmission network coding, make this algorithm be difficult to widespread use. In order to realize low complex degree relay reception algorithm, the linear receiving algorithm based on decoding transmission network coding is employed. Such as ZF (zeroforcing, ZF) and minimum mean-squared error (minimummeansquareerror, MMSE) receiving algorithm. Simultaneously, in order to improve the error performance of relay reception signal further, reduce the complexity of network-encoding operation, physically based deformation layer network coding (physical-layernetworkcoding, PNC) log-likelihood ratio (loglikelihoodratio, LLR) merges algorithm and is employed. First this algorithm obtains the decision statistics of Received signal strength by linear detection algorithm and calculates Soft Inform ation, then calculates the log-likelihood ratio of different transmission symbol and obtains final court verdict by the likelihood ratio criterion of physically based deformation layer network coding. But, the LLR merging algorithm based on PNC still has bigger gap compared to the ML receiving algorithm based on decoding transmission network coding on error performance.

Therefore, visible based on above analysis, when complexity decreases, the urgent receiving algorithm needing a kind of close optimum error performance.

In the last few years, owing to evidence theory (Dempster-Shaferevidencetheory, D-S) is in pattern recognition, the fields such as Intelligent Fusion obtain good performance, so studied person pays close attention to widely. Evidence theory is that a kind of broad sense Bayes explained based on structure type probability is theoretical, and the deduction of probability not only to be emphasized the objectivity of evidence but also to be emphasized the subjectivity that evidence is estimated by its theoretical explanation. So it can describe the uncertainty that is assumed proposition well. In evidence theory, if a finite set comprising whole separate hypothesis proposition is combined into identification framework, the initial brief inference of each subset is expressed by set function basic brief inference (basicprobabilityassignment, BPA) function. Generally speaking, usually utilize probability density function to be referred to as the set of burnt unit as a kind of phraseology of BPA function and basic reliability is not zero after being calculated by BPA function set. After the basic reliability determining each subset, the basic reliability of different evidence effect part of the body cavity below the umbilicus, housing the bladder, kidneys and bowels unit set is merged by the merging rule (Dempster ' srule) of recycling evidence theory. The merging rule of evidence theory can reduce each uncertainty assuming proposition greatly, thus obtains accurate result.

In sum, the main purpose of the present invention evidence theoretical algorithm is introduced multiple antennas bi-directional relaying system and encodes fusion with decoding transmission network, when complexity decreases, relay reception end is obtained close to optimum error performance.

Summary of the invention

In order to realize the error performance of approximate optimum receiving algorithm under relatively low complexity, the present invention provides a kind of theoretical reception method of multiple antennas bi-directional relaying evidence based on decoding transmission network coding. Evidence theory is the uncertainty utilizing basic brief inference function representation decline channel and noise to produce, and merge, by evidence theory, the uncertainty that rule reduces Received signal strength at receiving end, obtain reliable transmission signal eventually through maximum value judgement criterion or smallest point judgement criterion.

The main purpose of the present invention is the receptivity that the theoretical combination with decoding transmission network coding improves bi-directional relaying receiving end by evidence. For achieving the above object, the technical solution used in the present invention is: first set up the multiple antennas bi-directional relaying system model not containing direct link; Then, set up the mathematical model based on evidence theory; Finally, by evidence, the theoretical combination with decoding transmission network coding designs a relay reception method and analyzes the performance of proposed method.

The technical solution adopted in the present invention comprises the following steps:

Step 1, sets up the multiple antennas bi-directional relaying system model not containing direct link.

Multiple antennas bi-directional relaying system contains n by two single antenna users and one_RThe bi-directional relaying composition of root antenna. This system many locations stage model is equivalent to virtual MIMO system and represents:

Y=Hx+n (1)

In formula (1), H represents a n_RThe channel matrix of �� 2 dimensions, n_R>=2 expression relay reception antenna number, it is 0 that matrix element is modeled as average, and variance is independent identically distributed multiple Gauss's variable of 1;Representing the received signal vector of relay reception end, subscript T represents transposition;The transmission vector of two users represented, wherein x_iI=2 represents and sends the symbol that in vector x, i-th user sends, i.e. x₁Represent user S₁Transmission symbol, x₂Represent user S₂Transmission symbol, send vector element x_iTake from identical BPSK or QPSK constellation set ��.Representing that obeying average is 0, variance isWhite complex gaussian noise vector,Represent that a size is n_R��n_RUnit matrix. Define owing to degree of depth decline cannot directly communicate between user herein, namely not containing direct link; Communication channel between relaying and user is in a quasistatic flat-fading environment, and namely channel matrix H remains unchanged in a frame, independent variation between different frame, and channel condition information is known at receiving end, is unknown at sending end.

System model equivalence in formula (1) is written as

$\begin{array}{cc}{y}_i=h_{ij}{x}_j+\underset{\underset{l\≠j}{l=1}}{\overset{2}{\Σ}}{h}_{il}{x}_l+n_i,i=1,\mathrm{...},n_R& j=1,2\end{array}---\left(2\right)$

In formula (2), y_iRepresent the Received signal strength on i-th receiving antenna in bi-directional relaying; x_jRepresent user S_jTransmission symbol; h_ij,h_ilRepresent the element in channel matrix H.

Step 2, sets up the mathematical model of evidence theory.

Step 2.1, the determination of identification framework.

Owing to two users adopt identical modulating mode, therefore the constellation modulation that the determined identification framework of relay reception end should be corresponding is gathered. Therefore, if constellation set �� used is identification framework. Due to the impact of complexity, only consider the burnt unit of the single-point in identification framework �� set A₁With two point set A₂As calculating object.

Step 2.2, it is determined that the phraseology of basic brief inference function.

Key concept according to evidence theory is it will be seen that basic brief inference function m () expresses the original allocation of the reliability that evidence is set up, and meets following condition:

M (��)=0 (3)

$\∀A\⋐\mathrm{\Ψ},m\left(A\right)\≥0---\left(4\right)$

$\underset{\∀A\⋐\mathrm{\Ψ}}{\Σ}m\left(A\right)=1---\left(5\right)$

Wherein, A represents any one subset in identification framework ��; �� represents for empty set. According to above-mentioned condition, in definition identification framework ��, the basic brief inference function of each subset can be calculated by the conditional probability density function of relay Received signal strength. Owing to channel in this model and noise all obey multiple Gaussian distribution, so the conditional probability density function of Received signal strength represents it is:

$f\left(r\right|\mathrm{\α}\left(A\right))=\frac{1}{\sqrt{2{\mathrm{\π\σ}}^2}}\exp \left(\frac{-\left|\right|r-\mathrm{\α}\left(A\right)|{|}^2}{2{\mathrm{\σ}}^2}\right)---\left(6\right)$

In formula (6), r represents stochastic variable; �� (A) represents the eigenwert of stochastic variable r, i.e. the expectation of r; ��²Represent the variance of stochastic variable r.

Step 3, calculates the estimated value of each user on the every root receiving antenna of bi-directional relaying.

Step 3.1, utilizes linear detection algorithm to obtain the estimation initial value of each user on relay reception antenna.

The estimation initial value utilizing ZF linear detection algorithm to obtain each user on relay reception antenna can be represented further by formula (7):

${\tilde{x}}_j=w_{j}y=x_j+w_{j}n,j=1,2---\left(7\right)$

In formula (7), w_jRepresent the jth row vector of ZF pre-coding matrix,Represent the initial value of each user obtained by ZF detection.

Step 3.2, utilizes interference delete algorithm to obtain the estimation initial value of each user on the every root receiving antenna of relaying.

Each user is at the n of relay_RIndividual decision statistics can represent:

${\hat{x}}_{ij}=h_{ij}^{-1}(y_i-\underset{\underset{k\≠j}{k=1}}{\overset{2}{\Σ}}{h}_{ik}{\tilde{x}}_k),i=1,\mathrm{...},n_R,j=1,2---\left(8\right)$

By formula (2), formula (7) substitutes into the decision statistics that can obtain each user on every root receiving antenna in formula (8)Expression is:

Equivalent noise in formula (9)Can represent further and be:

Step 4, utilizes evidence theoretical algorithm to calculate identification framework �� according to Received signal strength on the every root antenna of relaying and is comprised burnt unit set A₁,A₂Basic reliability.

Under BPSK modulates, for all burnt units set A, the Received signal strength of jth user on i-th receiving antennaProbability density function can further represent by formula (6) and be:

In formula (12), �� (A) represents the average of burnt unit set.

Owing to basic brief inference function is 2^��Set function on [0,1], namely meets the condition of formula (5). Therefore, the basic brief inference function representation of jth the user's Jiao Yuan set A on i-th receiving antenna of relaying is:

$m_{ij}\left(A\right)=R_{ij}\·f\left({\hat{x}}_{ij}\right|\mathrm{\α}\left(A\right)),\∀A\⋐U---\left(13\right)$

In formula (13), U represents the general collection of all burnt units set; R_ijFor normalization coefficient, represent and it be:

$R_{ij}=1/{\Σ}_{\∀A\⋐U}f\left({\hat{x}}_{ij}\right|\mathrm{\α}\left(A\right))---\left(14\right)$

Step 5, utilizes evidence theory to merge rule to the single-point burnt unit set A of different user on different receiving antenna₁Merge. Merging rule according to evidence theory, the burnt unit of the single-point after merging set A₁Basic reliability represent and be:

$\begin{array}{c}\∀A_1\⋐\mathrm{\Ψ},A_1\≠\mathrm{\Φ}\\ m\left(A_1\right)=K\·\underset{A^1\∩\mathrm{...}\∩A^n=A_1}{\underset{A^1\mathrm{...}{A}^n\⋐\mathrm{\Θ}}{\Σ}}{m}_1\left(A^1\right)\mathrm{......}{m}_n\left(A^n\right)\end{array}---\left(15\right)$

In formula (15), normalization coefficient K represents and is:

$K={\left(\underset{A^1\∩\mathrm{...}\∩A^n\≠\mathrm{\Φ}}{\underset{A^1\mathrm{...}{A}^n\⋐\mathrm{\Θ}}{\Σ}}{m}_1\right(A^1\left)\mathrm{......}{m}_n\right(A^n\left)\right)}^{-1}---\left(16\right)$

Finally, by formula (15), (16) can obtain all single-points burnt unit set A in identification framework ��₁Basic reliability m (A₁)��

Step 6, obtains the final court verdict of each user by maximum value criterion. Namely each user's single-point burnt unit set A after merging is found out₁Basic reliability m (A₁) in maximum value, the single-point set A of its correspondence₁It is final court verdict reliably. Bit stream information is obtained finally by corresponding demodulation mode.

Step 7, obtains last network coded message finally by bit stream information that is different or two users.

Step 8, method analysis of complexity

The algorithm complex that present method proposes determines with the quantity of the basic reliability merged primarily of required calculating. When only considering single-point and 2 burnt unit's set, identification framework containsProposition is assumed in individual judgement, and M represents the size of identification framework. Here the basic reliability that definition calculates under a basic reliability or merging two different evidence effects is a basic brief inference unit. The complexity of a basic brief inference unit is O (M²), the complexity being carried algorithm by calculating known present method is O (M²n_Rn_t). And the complexity of ML algorithm isIt can thus be seen that put forward the complexity of algorithm much smaller than ML algorithm, good performance and the diversity gain identical with ML algorithm can also be obtained simultaneously.

In sum, compared with prior art, the present invention has the following advantages:

The present invention proposes a kind of theoretical reception method of multiple antennas bi-directional relaying evidence based on decoding transmission network coding. Compared to the linear algorithm forwarded based on decoding with based on the sub-optimal algorithm such as LLR algorithm of PNC, it is possible not only to significantly reduce Received signal strength and obtains uncertain and improve error performance, and obtain bigger performance gain.

Accompanying drawing explanation

Fig. 1, the multiple antennas bi-directional relaying evidence theory based on decoding transmission network coding proposed by the invention receives method flow diagram.

Fig. 2, not containing the multiple antennas bi-directional relaying system model schematic diagram of direct link.

Fig. 3, with the comparison diagram of existing algorithm error performance the present invention comprises 2 receiving antennas and the employing BPSK modulation of all nodes at relaying node. In figureRepresent that the present invention is set forth the bit error ratio curve of algorithm,Represent the bit error ratio curve of the ZF receiving algorithm based on decoding transmission network coding,Represent the bit error ratio curve of the LLR receiving algorithm of physically based deformation layer network coding,Represent the bit error ratio curve of the ML receiving algorithm based on decoding transmission network coding.

Fig. 4 and Fig. 5 be the present invention respectively under repeat packets is modulated containing the QPSK of 2 receiving antennas and repeat packets modulate containing the BPSK of 3 antennas under with the comparison diagram of existing algorithm performance. Wherein, the representation of curve is consistent with Fig. 3 Suo Shi.

Embodiment

Below in conjunction with drawings and Examples, inventive algorithm is described further.

The present invention is set forth method flow diagram as shown in Figure 1, comprises the following steps:

Step 1, sets up the multiple antennas bi-directional relaying system model not containing direct link.

Set up one and contain n by two single antenna users and one_RThe bi-directional relaying of=2 antennas forms uncoded equivalent virtual MIMO model as shown in Figure 2. This model can represent: y=Hx+n. It is 0 that the element of channel matrix H is modeled as average, and variance is the independent identically distributed multiple gaussian random variable of 1; Send vector x to obtain through BPSK or QPSK modulation by the 0 of stochastic generation, 1 stream of bits, and it is 1 by transmitting antenna energy normalized. White complex gaussian noise vector n average is 0, and variance isNoise varianceCan obtain by receiving symbol signal to noise ratio. Receiving symbol signal to noise ratio is defined as E_s/N₀, wherein E_sRepresent the average energy of relaying each receiving symbol of node, N₀For noise power spectral density. For white Gaussian noise, noise power spectral density N₀Equal noise varianceTherefore, receiving symbol signal to noise ratio E_s/N₀Can be written as

$E_s/N_0=m*n_R*E_t/(n_R*{\mathrm{\σ}}_N^2)=m*E_t/{\mathrm{\σ}}_N^2---\left(15\right)$

In formula, n_RBeing relay reception antenna number, m sends number of days and user's number. E_tFor sending signal energy, it is normalized to 1. Therefore noise varianceCan obtain by formula (15). Defining a quasistatic flat-fading environment, namely channel matrix H remains unchanged in a frame, independent variation between different frame. And, it is assumed that the status information of channel matrix H is known at relay reception end, and is unknown at user's sending end.

Step 2, selective recognition framework also determines the calculation expression of basic brief inference function: by modulation constellation atlas BPSK or QPSK of all nodes, the identification framework after namely determining is modulation constellation atlas ��. For BPSK modulation, the set of single-point burnt unit comprises A₁={ 1}, A₁={-1}, 2 burnt unit set A₂={ 1 ,-1}. Considering the impact of algorithm complex, single-point and the set of 2 burnt units are only considered in QPSK modulation, and namely the set of single-point burnt unit comprises A₁={ 1+j}, A₁={-1+j}, A₁={ 1-j}, A₁={-1-j}, 2 burnt unit set A₂={ 1+j, 1-j}, A₂={ 1+j ,-1+j}, A₂={ 1+j ,-1-j}, A₂={ 1-j ,-1+j}, A₂={ 1-j ,-1-j}, A₂={-1-j ,-1+j}. According to the Initialize installation of channel and noise, the conditional probability density function of final selection gaussian random variable is as the basic brief inference function representation form of calculating.

Step 3, determines the Signal estimation initial value of each user of relaying according to formula (7). And by formula (8), (9) calculate the Signal estimation value of each user on the every root antenna of relaying.

Step 4, according to formula (12), (13), (14) calculate the burnt unit set A of each user on the every root antenna of relaying under BPSK and QPSK respectively₁,A₂Basic reliability.

Step 5, utilizes formula (15), and (16) are to single-point burnt unit set A on different receiving antenna₁Basic reliability merge.

Step 6, obtains last court verdict by maximum value criterion: find out single-point burnt unit set A after merging₁Basic reliability m (A₁) in maximum value, be final court verdict.

Step 7, demodulation exports

The judgement symbol of gained is obtained corresponding bit stream information by the demodulation mode demodulation corresponding to modulation system.

The present invention's the Realization of Simulation on PC uses MATLAB language to programme. MATLAB is a kind of senior matrix language, comprises control statement, function, data structure, input and output and towards object programming feature, is the set comprising a large amount of computational algorithm. It has in more than 600 engineering the mathematical operation function to be used, it is possible to realize the various computing functions needed for user easily.

Fig. 3 comprises two single antenna users and one containing in the BPSK modulating system of the bi-directional relaying of 2 antennas, the comparison diagram of algorithm proposed by the invention and existing algorithm decoding performance. In figure, X-coordinate is symbol signal to noise ratio, and ordinate zou is bit error ratio. As can be seen from the figure, the error performance based on the theoretical receiving algorithm of multiple antennas bi-directional relaying evidence of decoding transmission network coding proposed by the invention is better than the performance of the LLR receiving algorithm of the ZF receiving algorithm based on decoding transmission network coding and physically based deformation layer network coding. It is 10 in bit error ratio^-2During the order of magnitude, obtain the performance gain of 6dB compared to the LLR receiving algorithm that physically based deformation layer network encodes based on the theoretical receiving algorithm of the multiple antennas bi-directional relaying evidence decoding transmission network coding. Meanwhile, compared to the ZF receiving algorithm based on decoding transmission network coding, the theoretical receiving algorithm of multiple antennas bi-directional relaying evidence based on decoding transmission network coding obtains the performance gain close to 8dB.

Fig. 4 and Fig. 5 be inventive algorithm respectively under repeat packets is modulated containing the QPSK of 2 receiving antennas and repeat packets modulate containing the BPSK of 3 antennas under with the comparison diagram of existing algorithm. As can be seen from the figure, along with increasing or the increase of receiving antenna number of number of constellation points, the error performance of algorithm set forth in the present invention is still better than the performance of the LLR receiving algorithm of the ZF receiving algorithm based on decoding transmission network coding and physically based deformation layer network coding. It is 10 in bit error ratio^-2During the order of magnitude, the LLR receiving algorithm that algorithm set forth in the present invention encodes compared to physically based deformation layer network obtains the performance gain close to 3dB, simultaneously, compared to the ZF receiving algorithm based on decoding transmission network coding, the theoretical receiving algorithm of multiple antennas bi-directional relaying evidence based on decoding transmission network coding obtains the performance gain close to 5dB. This shows, the conclusion of Fig. 4 and Fig. 5 gained and the conclusion of Fig. 3 are consistent.

Claims (1)

1., based on the theoretical reception method of multiple antennas bi-directional relaying evidence of decoding transmission network coding, first present method sets up the multiple antennas bi-directional relaying system model not containing direct link; Then, set up the mathematical model based on evidence theory; Finally, by evidence, the theoretical combination with decoding transmission network coding designs a multiple antennas bi-directional relaying reception method and analyzes the performance of proposed method;

It is characterized in that: present method comprises the following steps,

Step 1, sets up the multiple antennas bi-directional relaying system model not containing direct link;

Multiple antennas bi-directional relaying system contains n by two single antenna users and one_RThe bi-directional relaying composition of root antenna; This system many locations stage model is equivalent to virtual MIMO system and represents:

Y=Hx+n (1)

In formula (1), H represents a n_RThe channel matrix of �� 2 dimensions, n_R>=2 expression relay reception antenna number, it is 0 that matrix element is modeled as average, and variance is independent identically distributed multiple Gauss's variable of 1;Representing the received signal vector of relay reception end, subscript T represents transposition;The transmission vector of two users represented, wherein x_iI=2 represents and sends the symbol that in vector x, i-th user sends, i.e. x₁Represent user S₁Transmission symbol, x₂Represent user S₂Transmission symbol, send vector element x_iTake from identical BPSK or QPSK constellation set ��;Representing that obeying average is 0, variance isWhite complex gaussian noise vector,Represent that a size is n_R��n_RUnit matrix; Define owing to degree of depth decline cannot directly communicate between user herein, namely not containing direct link; Communication channel between relaying and user is in a quasistatic flat-fading environment, and namely channel matrix H remains unchanged in a frame, independent variation between different frame, and channel condition information is known at receiving end, is unknown at sending end;

System model equivalence in formula (1) is written as

$y_i=h_{ij}{x}_j+\underset{l\≠j}{\overset{2}{\underset{l=1}{\mathrm{\Σ}}}}{h}_{il}{x}_l+n_i,i=1,...,n_R,j=1,2---\left(2\right)$

In formula (2), y_iRepresent the Received signal strength on i-th receiving antenna in bi-directional relaying; x_jRepresent user S_jTransmission symbol; h_ij,h_ilRepresent the element in channel matrix H;

Step 2, sets up the mathematical model of evidence theory;

Step 2.1, the determination of identification framework;

Owing to two users adopt identical modulating mode, therefore the constellation modulation that the determined identification framework of relay reception end is corresponding is gathered; Therefore, if constellation set �� used is identification framework; Due to the impact of complexity, only consider the burnt unit of the single-point in identification framework �� set A₁With two point set A₂As calculating object;

Step 2.2, it is determined that the phraseology of basic brief inference function;

Key concept according to evidence theory is it will be seen that basic brief inference function m () expresses the original allocation of the reliability that evidence is set up, and meets following condition:

M (��)=0 (3)

$\∀A\⋐\mathrm{\Ψ},m\left(A\right)\≥0---\left(4\right)$

$\underset{\∀A\⋐\mathrm{\Ψ}}{\Σ}m\left(A\right)=1---\left(5\right)$

Wherein, A represents any one subset in identification framework ��; �� represents for empty set; According to above-mentioned condition, in definition identification framework ��, the basic brief inference function of each subset can be calculated by the conditional probability density function of relay Received signal strength; Owing to channel in this model and noise all obey multiple Gaussian distribution, so the conditional probability density function of Received signal strength represents it is:

$f\left(r\right|\mathrm{\α}\left(A\right))=\frac{1}{\sqrt{2{\mathrm{\π\σ}}^2}}\exp \left(\frac{-\left|\right|r-\mathrm{\α}\left(A\right)|{|}^2}{2{\mathrm{\σ}}^2}\right)---\left(6\right)$

In formula (6), r represents stochastic variable; �� (A) represents the eigenwert of stochastic variable r, i.e. the expectation of r; ��²Represent the variance of stochastic variable r;

Step 3, calculates the estimated value of each user on the every root receiving antenna of bi-directional relaying;

Step 3.1, utilizes linear detection algorithm to obtain the estimation initial value of each user on relay reception antenna;

The estimation initial value utilizing ZF linear detection algorithm to obtain each user on relay reception antenna can be represented further by formula (7):

${\tilde{x}}_j=w_{j}y=x_j+w_{j}n,j=1,2---\left(7\right)$

In formula (7), w_jRepresent the jth row vector of ZF pre-coding matrix,Represent the initial value of each user obtained by ZF detection;

Step 3.2, utilizes interference delete algorithm to obtain the estimation initial value of each user on the every root receiving antenna of relaying;

Each user is at the n of relay_RIndividual decision statistics can represent:

${\hat{x}}_{ij}=h_{ij}^{-1}(y_i-\underset{k\≠j}{\overset{2}{\underset{k=1}{\mathrm{\Σ}}}}{h}_{ik}{\tilde{x}}_k),i=1,...,n_R,j=1,2---\left(8\right)$

By formula (2), formula (7) substitutes into the decision statistics that can obtain each user on every root receiving antenna in formula (8)Expression is:

Equivalent noise in formula (9)Can represent further and be:

Step 4, utilizes evidence theoretical algorithm to calculate identification framework �� according to Received signal strength on the every root antenna of relaying and is comprised burnt unit set A₁,A₂Basic reliability;

Under BPSK modulates, for all burnt units set A, the Received signal strength of jth user on i-th receiving antennaProbability density function can further represent by formula (6) and be:

In formula (12), �� (A) represents the average of burnt unit set;

Owing to basic brief inference function is 2^��Set function on [0,1], namely meets the condition of formula (5); Therefore, the basic brief inference function representation of jth the user's Jiao Yuan set A on i-th receiving antenna of relaying is:

$m_{ij}\left(A\right)=R_{ij}\·f\left({\hat{x}}_{ij}\right|\mathrm{\α}\left(A\right)),\∀A\⋐U---\left(13\right)$

In formula (13), U represents the general collection of all burnt units set; R_ijFor normalization coefficient, represent and it be:

$R_{ij}=1/{\mathrm{\Σ}}_{\∀A\⋐U}f\left({\hat{x}}_{ij}\right|\mathrm{\α}\left(A\right))---\left(14\right)$

Step 5, utilizes evidence theory to merge rule to the single-point burnt unit set A of different user on different receiving antenna₁Merge; Merging rule according to evidence theory, the burnt unit of the single-point after merging set A₁Basic reliability represent and be:

$\begin{array}{c}\∀A_1\⋐\mathrm{\Ψ},A_1\≠\mathrm{\Φ}\\ m\left(A_1\right)=K\·\underset{A^1\∩...\∩A^n=A_1}{\underset{A^1...A^n\⋐\mathrm{\Θ}}{\mathrm{\Σ}}}{m}_1\left(A^1\right)......m_n\left(A^n\right)\end{array}---\left(15\right)$

In formula (15), normalization coefficient K represents and is:

$K={\left(\underset{A^1\∩...\∩A^n\≠\mathrm{\Φ}}{\underset{A^1...A^n\⋐\mathrm{\Θ}}{\mathrm{\Σ}}}{m}_1\right(A^1)......m_n(A^n\left)\right)}^{-1}---\left(16\right)$

Finally, by formula (15), (16) can obtain all single-points burnt unit set A in identification framework ��₁Basic reliability m (A₁);

Step 6, obtains the final court verdict of each user by maximum value criterion; Namely each user's single-point burnt unit set A after merging is found out₁Basic reliability m (A₁) in maximum value, the single-point set A of its correspondence₁It is final court verdict reliably; Bit stream information is obtained finally by corresponding demodulation mode;

Step 7, obtains last network coded message finally by bit stream information that is different or two users;

Step 8, method analysis of complexity

The algorithm complex that present method proposes determines with the quantity of the basic reliability merged primarily of required calculating; When only considering single-point and 2 burnt unit's set, identification framework containsProposition is assumed in individual judgement, and M represents the size of identification framework; Here the basic reliability that definition calculates under a basic reliability or merging two different evidence effects is a basic brief inference unit; The complexity of a basic brief inference unit is O (M²), the complexity being carried algorithm by calculating known present method is O (M²n_Rn_t); And the complexity of ML algorithm isIt can thus be seen that put forward the complexity of algorithm much smaller than ML algorithm, good performance and the diversity gain identical with ML algorithm can also be obtained simultaneously.